In the first place, there should be no policy in the company that does not contribute its proportionate share of the expense allowance during every year of its life. I make a special point of this, for at present the policies which have become paid up, either by the payment of a single premium at the outset or by the completion of a stipulated number of payments, contribute practically nothing to the expense account after the premium payments cease.

The following plan, I think, complies with all the requirements of the problem. By the proposed method every policy, at all stages of its existence, contributes its exact share to the expense fund, whatever its plan of payment may be.

Let us, as an illustration, examine the case of a ten year endowment policy, taken out at age 30, and consider it under three aspects, first, as paid for in advance by a single payment, second, as paid by five annual payments, and third, as paid for annually throughout the term. I have used this short term endowment policy simply for convenience, the rule applying equally to policies of longer term or to the ordinary life policy, which is, in fact, an endowment policy payable at death or age 100.1

Taking the case of the single premium endowment policy for $1,000, we find that the following sums are required, each year to provide for the care of the reserve and to pay the government fees (1 per cent. of reserve):

1styear$6.99826thyear$8.4136
2d"7.25607th"8.7381
3d"7.52588th"9.0781
4th"7.80829th"9.4346
5th"8.103910th"9.8086

The insurance expenses should be covered by the 20 per cent. allowance given below:

1styear$ .44226thyear$ .2566
2d".41007th".2076
3d".37628th".1556
4th".34029th".0988
5th".299610th".0344

Consequently the total contribution required from this policy each year is:

1styear$7.44046thyear$8.6702
2d"7.66607th"8.9457
3d"7.90208th"9.2337
4th"8.14849th"9.5334
5th"8.403410th"9.8430

The present value of all these contributions is found to be, at 4 per cent. interest, $71.6394; in other words, this sum paid at the outset, provides a fund from which we may deduct the current expenses of each year in advance, and by accumulating the balance at the assumed rate of interest from year to year, we shall have enough to pay the anticipated expenses, leaving nothing over.

In the above case the sums in hand at the beginning of the year are as follows:

1styear$71.36946thyear$42.6981
2d"66.76697th"35.3890
3d"61.46508th"27.5009
4th"55.70559th"18.9979
5th"49.459410th"9.8430

We find a somewhat different condition existing during the first years of a 5-year endowment policy. As there is more insurance and less banking, the requirements are as follows:

1 P. Ct.
on Reserve.
20 P. Ct.
on Cost.
Total.Initial Fund.
1styear$1.5038$1.2572$2.7610$12.9769
2d"3.04061.02164.062223.6015
3d"4.6503.78525.435533.2979
4th"6.3367.53786.874541.9538
5th"8.1039.29968.403549.4594
6th"8.4136.25668.670242.6981
7th"8.7381.20768.925735.3890
8th"9.0781.15569.233727.5009
9th"9.4346.09889.533418.9979
10th"9.8086.03449.84309.8430

As the premium payments extend over only five years, the expense contributions must all be paid during that time and are most conveniently made by a uniform addition to the net premium.

The present value of the amounts in column 3 is $60.0819, and the equivalent annuity for five years is $12.9769. This amount, received for five consecutive years, will put the company in funds to pay current expenses and leave a reserve of $42.6981 at the beginning of the sixth year, which, as we have seen in the analysis of the single-premium policy, is the sum required for future expenses on the paid up basis.

In like manner we find that the 10-year annuity equivalent to the present value of the annual contributions in the case of an annual-payment policy is $5.534, thus:

1 P. Ct.
on Reserve.
20 P. Ct.
on Cost.
Total.Initial Fund.
1styear$.8234$1.3514$2.1748$ 5.5340
2d"1.64731.24782.89519.0275
3d"2.50961.13883.648411.9116
4th"3.41241.02104.433414.1277
5th"4.3572.89165.248815.6161
6th"5.3479.75346.101316.3160
7th"6.3853.59666.981916.1572
8th"7.4726.42707.899615.0763
9th"8.6127.24188.854512.9977
10th"9.8086.03449.84309.8430

The present value of the ten yearly expense items given in the "total" column above is $46.6812, which is equal to a ten-year annuity of $5.534. The several premiums stand now as follows:

ENDOWMENT: $1,000, AGE 30, PAYABLE AT DEATH OR 40

Net Prem.2Margin.Total.
At single premium.$687.228$71.6394$758.8674
At five premiums.150.61512.9769163.5939
At annual premiums.84.1725.534089.7060

By the actuaries' rate we have, with the customary loading for expense:

Single premium: $721.66 (loaded, $34.36). Five premiums, $188.70 (loaded $37.78). Annual premium, $105.65 (loaded $21.11).

Admitting the correctness of the new method, we must conclude that the present single premium is not sufficiently loaded to cover its own expenses, while the annual payment policy pays more than its just share. A prominent and thoroughly informed life insurance president says in this connection: "Many of the policies, particularly the short term endowments, are charged with too high a percentage of expenses to prove a good investment at maturity or profitable to the insured in case of surrender." This is not to be wondered at when the applicant for a 10-year endowment policy sees at a glance that he must pay, in the gross, more than is returned unless he should die in the interim, in which case a plain "life" or "term" policy would have answered the purpose. Under the new system of assessing expenses one form is as desirable as another, from the standpoint of the insured or the company.

The new premium for the 10-year endowment policy, $89.71, commends itself at once to the applicant, who can easily see that his total outlay must fall short of the amount ultimately to be realized, of course, disregarding interest and probable dividends in both cases.

In discounting the future expense contributions I have not taken the chances of dying into account. Hence the expense reserve in any instance applies only to that individual case, and, in the event of death or surrender before the maturity of the policy, the amount of the expense fund not used would naturally revert to the insured.

The scheme of expense assessment outlined above will doubtless be pronounced impracticable by the majority of insurance men.

Such a far reaching reform is too much to hope for, at least in the immediate future.

No well informed life insurance expert will deny that there are opportunities for improvement in the business, but to graft new methods on old companies is a hopeless undertaking.

It is well, however, to have new methods well matured in advance of the public demand, and I feel convinced that the ideas here set forth are in the line of the reform which, before long, must be instituted by the companies if they would retain the confidence and patronage of the community.

Doubtless many insurance presidents could tell of suggestions which have impressed them favorably and which they would gladly have adopted were it not for the injustice done thereby to older members and the changes necessary to bring existing contracts into conformity with the new system. Similar objections may be urged against the ideas here advanced, and I must confess I hardly see a way by which the present suggestions can be utilized by existing companies. We can only hope that sooner or later some of the new theories may be practically tested. Meanwhile the companies at present in the field are doing a great work for the good of humanity, even though their methods may be, in some particulars, more practical than scientific.

Winchester, Mass.FRANK J. WILLS.
[1]The expense allowance on a plain life policy for $1,000, taken at age 33, would be about $5.29; net premium (com. ex. 4 per cent.), $18.04; total office premium, $23.33; present rate $24.10.[2]Thirty American offices. Discount from middle of year, Vx-½ or (M x 1.01961) / Dx.